There are at least three Mayan calendars. I was listening to the How Stuff Works: Mayan Calendar podcast, and learned that the Mayan calendars are not as strange as I expected them to be. Let’s first look at how our years are structured:

1millenium

9century

5decade

7year

When the last component overflows (from 9 to 0), we carry one and increment the decade. When the decade overflows we increment the century. This is how base 10 numbers work.

Now let’s look at how dates are structured:

1957year

Julmonth

23day

When the last component (day) overflows from 31 to 1, we carry one and increment the month. When the month overflows from Dec to Jan, we increment the year. This is very similar to how base 10 numbers work, except that each component has its own rules for when it overflows, and months don’t all have the same number of days.

How are weekdays numbered? We can say both the day of week and the day of month, and increment both each day:

Tuesdayweekday

the 23rdday of month

The Mayan Tzolk’in calendar works like this. Both components are incremented each time. One component has 20 days and the other has 13 days, and they line up every 260 days.

12trecena

Lamatday name

The Mayan Haab calendar is more conventional, lasting 365 days. There are 18 months each with 20 days, giving 360 days, plus an extra 5 days to make it fill a year. They didn’t handle leap years.

17month

K’ayabday

The Mayan Long Count calendar is the one people are worked up over. There are five (or maybe nine) “digits”, each base 20 except one that’s base 18 to match the months of the Haab calendar. However the Long Count calendar doesn’t include the extra 5 days, so it doesn’t stay lined up with Haab.

12baktun

19katun

19tun (year)

17uinal (month)

15kin (day)

What’s the big deal about 21 Dec 2012? It’s 13.0.0.0.0, at least under the most common translation of our calendar to the Mayan calendar. It’s sort of like how people celebrated the year 2 0 0 0. It’s nice to celebrate a bunch of zeros. Some interpretations say that it doesn’t go to 13.0.0.0.0 but resets back to 0.0.0.0.0, but it’s not universally agreed upon, and some say that there are four more places in the calendar system, so it’d be 0.0.0.0.13.0.0.0.0, resetting only after 63 million years.

In any case, the thing I find strangest about the Mayan calendar systems is that there are so many of them, somewhat incompatible with each other. In addition to the three I described above, there’s a 9 day cycle, a lunar cycle, a Venus cycle, and a few others. See the Wikipedia page for a reasonable overview. If you use Emacs, the Mayan calendar is included, and you can use M-: (calendar-mayan-date-string) to get back a string like "Long count = 12.19.19.17.15; tzolkin = 12 Men; haab = 18 Mac".